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    <title>det</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>det</b> -  determinant</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>det(X)  </tt>
      </dd>
      <dd>
        <tt>[e,m]=det(X)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>X</b>
        </tt>: real or complex square matrix, polynomial or rational matrix.</li>
      <li>
        <tt>
          <b>m</b>
        </tt>: real or complex number, the determinant base 10 mantissae</li>
      <li>
        <tt>
          <b>e</b>
        </tt>: integer, the determinant base 10 exponent</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
      <tt>
        <b>det(X)</b>
      </tt> ( <tt>
        <b>m*10^e</b>
      </tt> is the determinant of the square matrix <tt>
        <b>X</b>
      </tt>.</p>
    <p>
    For polynomial matrix <tt>
        <b>det(X)</b>
      </tt> is equivalent to <tt>
        <b>determ(X)</b>
      </tt>.</p>
    <p>
    For rational matrices <tt>
        <b>det(X)</b>
      </tt> is equivalent to <tt>
        <b>detr(X)</b>
      </tt>.</p>
    <h3>
      <font color="blue">References</font>
    </h3>
    <dl>
      <p>
     det computations are based on the Lapack routines
      DGETRF for  real matrices and  ZGETRF for the complex case.</p>
    </dl>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

x=poly(0,'x');
det([x,1+x;2-x,x^2])
w=ssrand(2,2,4);roots(det(systmat(w))),trzeros(w)   //zeros of linear system
A=rand(3,3);
det(A), prod(spec(A))
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="../polynomials/detr.htm">
        <tt>
          <b>detr</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../polynomials/determ.htm">
        <tt>
          <b>determ</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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